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# How to calculate the interquartile range

Updated May 03, 2018

The interquartile range, sometimes called the IQR, represents the range from the 25th percentile to the 75th percentile, or middle 50 per cent of a data set. The interquartile range can be used to show what the range of an average performance would be, such as where most people fall on a certain test or what the average employee makes. The interquartile range can be more effective than the mean or median because it shows the dispersion range rather than just one number.

Order your data points from least to greatest. For example, if your data points were 10, 19, 8, 4, 9, 12, 15, 11 and 20, you would rearrange them like this: {4, 8, 9, 10, 11, 12, 15, 19, 20}.

Determine the position of the first quartile using the following formula: (N+1)/4 where N is the number of points in the data set. If the first quartile falls between two numbers, take the average. In the above example, since there are nine data points, you would add 1 to 9 to get 10 and then divide by 4 to get 2.5. Since the first quartile falls between the second and third value, you would take the average of 8 and 9 to get 8.5.

Determine the position of the third quartile using the following formula: 3*(N+1)/4 where N is the number of points in the data set. If the third quartile falls between two numbers take the average. In the above example, since there are nine data points, you would add 1 to 9 to get 10, multiply by 3 to get 30 and then divide by 4 to get 7.5. Since the first quartile falls between the seventh and eighth value, you would take the average of 15 and 19 to get 17.

Calculate the interquartile range by subtracting the value of the first quartile (step 2) from the value of the third quartile (step 3). Finishing the example, you would subtract 8.5 from 17 to find that the interquartile range equals 8.5.

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